Update algorithms.py

pydatastructs/linear_data_structures/algorithms.py

@@ -12,6 +12,7 @@
     'matrix_multiply_parallel',
     'counting_sort',
     'bucket_sort',
+    'lcs',
 ]
 
 def _merge(array, sl, el, sr, er, end, comp):
@@ -546,3 +547,39 @@ def bucket_sort(array: Array, **kwargs) -> Array:
     if _check_type(array, DynamicArray):
         array._modify(force=True)
     return array
+##--------------------------------------------------------##
+# Dynamic Programming implementation of LCS problem 
+
+def lcs(X , Y): 
+    # find the length of the strings 
+    m = len(X) 
+    n = len(Y) 
+
+    # declaring the array for storing the dp values 
+    L = [[None]*(n+1) for i in range(m+1)]
+    ##The xrange() function in Python is used to generate a sequence of numbers, similar to the range() function. However, xrange() is used only in Python 2. x whereas range() is used in Python 3. x
+
+    """Following steps build L[m+1][n+1] in bottom up fashion 
+    Note: L[i][j] contains length of LCS of X[0..i-1] 
+    and Y[0..j-1]"""
+    for i in range(m+1): 
+        for j in range(n+1): 
+            if i == 0 or j == 0 : 
+                L[i][j] = 0
+            elif X[i-1] == Y[j-1]: 
+                L[i][j] = L[i-1][j-1]+1
+            else: 
+                L[i][j] = max(L[i-1][j] , L[i][j-1]) 
+
+    # L[m][n] contains the length of LCS of X[0..n-1] & Y[0..m-1] 
+    return L[m][n] 
+#end of function lcs 
+
+
+# Driver program to test the above function 
+X = "AGGTAB"
+Y = "GXTXAYB"
+print("Length of LCS is ", lcs(X, Y))
+##Output:
+##Length of LCS is 4
+##------------------------------------------------------------##